It’s a Small World, After All

We all know we’re only 7 steps away from Jonny Depp. Or Obama. Or Lionel Messi (maybe, quite literally if you’re here at the GSE.) However, the world is not only small; it is shrinking. We are becoming more interconnected through new forms of communication. We find out information through these networks, which then influences our decisions. What we do, therefore, is influenced by whom we know.

Matt Jackson at Stanford University has been analysing the increasing connectedness of the world and its implications on spreading information, and came to Barcelona to explain his findings at the UPF opening ceremony. (And there we were thinking we’d been here so long, you could look us up on the book directory at the library and know where to find us.)

So what is a network and how can we think about connectivity within one?

Jackson uses three central ideas to describe linkages within a group:

Density: how many people are connected to others within a given population. It is quite simply the average (mean) degree of connections made within the group. He gave some illustrative examples of popular networks:

– the average number of co-authors on an economics paper: 1.7; Biology paper: 15.5. Maybe homo economicus is as unfriendly as we’re told.

– the average number of friends someone may describe as ‘close’: 6.1.

– yes, he gave the Facebook statistics: the average Facebook user has 120 friends. Isn’t that how you got here, anyway?

Local Patterns: what matters here isn’t the number of connections one person has, but how important those connections are within the community. Yes, you might have the most number of friends, but will you spread the flu / news about the latest product / cat LOL to the rest of the population the fastest?

Jackson will do a little matrix algebra on you to figure out your eigenvector centrality to establish this. Just like how the original Google concept works, where pages are rated according to the number of links to them, and the number of links to the pages linked to those pages etc., so you can find the results for a network of people. You want your friends to have friends too, to boost your eigenvector credentials.

As one lecturer pointed out, finally we have a reason to listen in econometrics 101 now – we’ve linked it to Twitter.

Segregation: how groups interact within a group. Here, it’s about to whom you are linked, rather than to how many.

In studying high-school friendship groups, studies have found strong within-race connectivity patterns. In the data set used for illustration, black students were often friends within the black community, and whites within the white community. Hispanics were more or less evenly distributed between the two, but this was a smaller sub-group.

The idea here is that smaller groups will integrate better, but a once a critical mass has been reached, we see segregation. These results repeated across multiple study groups, and give rise to what is known as homophilia – liking what is like you.

So what?

The policy implications were not discussed in much depth, although Jackson raised a point which piqued my concern. Not only are we more connected than ever before, we can select the characteristics of those with whom we interact. Online fan sites for specific interest allow us to segregate and find others like us.

With the demonstrated tendency to homophilia, and a focus on making ‘friends in the right places’, well-connected special interest groups can gain influence. In contrast, we may think of solitude being associated to a tea-drinker, and sociability being associated with coffee-drinkers. If there is an even split between tea- and coffee-drinkers in the community, this model would suggest one group will be far better represented than another.

More realistically, since we know that only 1% of white Americans marry outside their race, perhaps we should be targeting this specific group as a bridge between two networks. In this way, we can spread information more quickly amongst sub-populations.

Economists have been studying the impacts of financial networks in the aftermath of the banking crisis, and Jackson also gave a separate lecture devoted to this topic. He presented a model of a cascade system, to interpret possible scenarios of network effects. For more information on the model and the findings, click here.

In the case of financial contagion we find a rather worrisome moral hazard: a firm might be incentivised to make a bad investment in order to increase bargaining power with an investor of theirs who can’t afford for them to fail. (Wait, this sounds familiar.) The model, however, seems to indicate this is only true when few firms are moderately integrated – perhaps, then, we need to shape policy to promote greater levels of diversification and integration.

For GSE students, the answer seems clear: download your LinkedIn statistics, and do a few sums. It turns out it’s not only who you know, but who they know, too.